Question

Solve the equation using quadratic formula.

$r^2+10r+25=0$

Short answer

The solution is$r=-5$.

Step-by-step solution

 Given Information.   

The given equation is $r^2+10r+25=0$.

Write the quadratic equation in standard form and identify  a,b,c.

$r^2+10r+25=0$

The quadratic equation is in standard form.

So,

$a=1,b=10,c=25$

Substitute the values in quadratic formula.   

$$\begin{gathered} r=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ r=\frac{-10\pm \sqrt{(10{)}^2-4(1\left)\right(25)}}{2\left(1\right)} \\ r=\frac{-10\pm \sqrt{100-100}}{2} \\ r=\frac{-10\pm \sqrt{0}}{2} \end{gathered}$$

The square root of zero is zero itself.

So,

$$\begin{gathered} r=\frac{-10}{2} \\ r=-5 \end{gathered}$$

Thus, the root is$r=-5$.